Sorry if it has been mentioned, I just skimmed, but it would also dependent on scene/context. Someone like Steven Erikson who is weaving this gargantuan epic history has so many characters it truly is astonishing. In certain sequences he jumps from head to head to head to head to head to head to head you get the point, but always when there is a good reason for it (like seeing a cataclysmic event or whatever through a number of differing POVs so the reader gets a multifaceted view of whatever is going on).
Martin gives each POV its own chapter so it is relatively easy to keep track of stuff (much easier than Erikson at any rate, who often can start new sequences without revealing who we are supposed to "look through").
Personally I think the more, the merrier

Erikson uses a third person omniscient format where his omniscient narrator can flick through viewpoints. Martin uses third person limited, keeping tight on one pov character per chapter. So that's part of it. If you do feel you need to have a lot of viewpoints on events in the story, third person omniscient can be a very useful technique for delivering multiple pov's quickly.

Not really, I find. I've worked with plenty of experienced, "good" authors who still have to go over their stuff to figure out if they've been unclear when they wanted to be clear and whether they need to cut something or someone, whether what's in their heads is down on the page and who have uncertainty about what's in their head in the first place or where things might be not working. Deciding how many characters to have in your story is not about measurements of talent; it's just about the process of writing and story crafting. Certainty or lack thereof about the decisions you make is not a reflection of writing ability or experience at making decisions. Lack of certainty about these things is pretty much normal for writers. Most writers will say that they'd go back and tinker with published works -- even award winning ones -- if they could (and occasionally they do for a new revised reissue.) What they were certain about in handling, they don't necessarily stay certain about. So any angle of attacking the issue can be potentially useful and it's usually, I find, not a good idea to assume an author knows of or has remembered an angle of attack he could use, even simple ones like, would cutting a character help. Sometimes the only way an author can figure things out and have the aha moment is from another person asking him questions. So MDM's questions may help or may not with the OP's original issue, depending on how useful they are with the OP's particular process.

If you do feel you need to have a lot of viewpoints on events in the story, third person omniscient can be a very useful technique for delivering multiple pov's quickly.

I absolutely agree, for what it's worth, but when does that cross the line into the cardinal sin (so I'm told) of "head hopping"?

This is something I was very guilty of in my earlier stuff, which I've now trained myself out of to the extent that I now only write in either third person limited or first person. How do you tell where the line is between an effective omniscient POV and "head hopping"?

I absolutely agree, for what it's worth, but when does that cross the line into the cardinal sin (so I'm told) of "head hopping"?

This is something I was very guilty of in my earlier stuff, which I've now trained myself out of to the extent that I now only write in either third person limited or first person. How do you tell where the line is between an effective omniscient POV and "head hopping"?

There isn't a line. "Head-hopping" is a term that was made up by people who don't like third person omniscient and don't think anyone should make use of that format ever anymore. So if you ever use the multiple pov technique, then you are head-hopping and for those with that preference, you are a bad, bad writer.

What you are talking about, though, is how do you handle multiple pov technique effectively and that depends first on whether you want to use it and have an omniscient narrator approach. You may not -- it may not work with your eventual style preferences. If you do, there are many uses for it. You can provide several points of view of say a big action scene like a battle without inserting section breaks in between them as you would do if you are using third person limited. That gives you a more seamless multi-person, multi-camera perspective. Multiple povs can also work well with a two person conversation in which you get both people's takes on a conversation in the same section. So, for instance, if you had a negotiation scene between a human and an alien, giving both their perspectives in the scene would allow readers to understand how they are analyzing what's been said and provide a lot of info beyond the dialogue, or beyond having one pov and then having to have the other pov provide info in flashback memory later. You could show how the two characters are completely misunderstanding each other as they talk. So for some purposes multiple pov can be a faster, more flowing narrative because it doesn't require the section breaks and big announcement therein of a change of pov.

One of the books I'm reading at the moment is Ari Marmell's The Goblin Corps and he uses omniscient multiple pov to be able to do big action scenes in which there are multiple characters in different locales or positions, specifically his squad of creatures. The narrative will ping pong, so if one character is attached to a rope lowered into a hole and others are up top holding the rope and a third is checking the horizon, he can just switch between them to integrate the whole scene. We get to know the characters just as well -- better in a sense since we're in all of their heads, not just a smaller segment of them, but he doesn't have to build separate action arcs for all of them with chapter and section breaks to do that. So it's an effective technique for what he's doing and omniscient techniques like multiple pov's are often used for satire because they can help in setting up a lot of action and humor aspects.

Human beings are perfectly able to process this info in text, in the same way that they can process jump cuts and split screens. The biggest issue is just making clear whose head you're in when you switch pov, which is done in relatively few words. You're just using the words instead of a section break to note pov change for them. Some readers, though, don't like the effect the technique produces. They just don't. That is, though, if they notice that you have it. A lot of people read third person omniscient narratives with omniscient narration and/or multiple pov's in a scene and they simply process the info without noticing the structure. I've had numerous conversations with people about omniscient texts they've read and liked that they're stunned to hear have evil head-hopping or an omniscient narrator, (or even a collective omniscient narration "we.") We are all very good at processing text and pov. How often you switch from one character to another involves what info you are providing, your goals for that section, what sort of pacing and action you're having, etc., so it's one of the many things that authors have to decide.

The OP, however, I don't think was concentrating on multiple pov so much as how many pov characters. And these questions are all related -- how many pov characters do you need for your story goals, how many times do you switch in a scene under multi pov for your story goals, etc. If Princeroth has six main characters whose viewpoint is tugging for attention (plus the occasional view from an antagonist,) it's not inherently unmanageable and can be done in third person limited format. But, depending on the narrative, an author might not want to limit pov switches to every chapter -- that may be too long and require too many extra chapters. So section breaks for the switch in perspective -- those couple of blank lines -- might be a more effective way to go, with more than one pov in each chapter. Chapter and section breaks can be used in omniscient formats as well to shift pov.